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FOPRA Experiment 38: Lieb-Robinson Bounds and Applications (QST-TH)

Course 0000100038 in SS 2024

General Data

Course Type practical training
Semester Weekly Hours 1 SWS
Organisational Unit Lab Courses in Physics
Lecturers Robert König
Severin Schraven
Simone Warzel
Michael Marc Wolf
Dates

Further Information

Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.

additional remarks How fast can information propagate through a quantum many-body system with local interactions? Lieb-Robinson bounds provide fundamental upper limits on the speed at which the dynamics of such a system can distribute initially localized information. In particular, these bounds give a “speed limit” called the Lieb-Robinson velocity.Applications of Lieb-Robinson bounds are numerous; including multi-dimensional Lieb-Schultz-Mattis theorems, exponential clustering in gapped ground states, area laws, the analysis of quantum phases of matter, the complexity of states and many, many more.In this project, you will learn how to formalize the question of information propagation in terms of basic quantum-mechanical concepts such as Heisenberg-evolved operators and operator norms of commutators. Following a list of instructions, you will then develop a mathematicalproof of this fundamental result.As applications you may consider consequences of Lieb-Robinson bounds to the problem of state preparation or to topological order.In the first application you will show that certain highly entangled states such as the GHZ-state cannot be generated by a locally generated unitary in constant time from a product state.This result can also be reinterpreted a circuit depth lower bound on preparation circuits and thus immediately connects to complexity-theoretic questions in quantum computing.Another application concerns Kitaev’s toric code, a local stabilizer Hamiltonian on a 2D lattice of qubits whose ground states satisfy a condition called topological quantum order (TQO): no local observable can distinguish orthogonal ground states. While TQO is immediately connected to quantum error correction via the so-called Knill-Laflamme conditions, here you will study another key consequence of TQO derived from Lieb-Robinson bounds: preparing ground states of the toric code from a product state using locally generated unitary evolution requires a time scaling at least linearly in the (linear) system size.Overall, this project will help familiarize yourself with a fundamental tool in quantum many-body systems and basic results in topological order.
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Equivalent Courses (e. g. in other semesters)

SemesterTitleLecturersDates
SS 2023 FOPRA Experiment 38: Lieb-Robinson Bounds and Applications (QST-TH) König, R. Warzel, S. Wolf, M.
SS 2022 FOPRA Experiment 38: Lieb-Robinson Bounds and Applications (QST-TH) König, R. Warzel, S. Wolf, M.
Assistants: Schulz, S.
WS 2021/2 FOPRA Experiment 38: Lieb-Robinson Bounds and Applications (QST-TH) König, R. Schulz, S. Warzel, S. Wolf, M.
SS 2021 FOPRA Experiment 38: Lieb-Robinson Bounds and Applications König, R. Warzel, S. Wolf, M.
Assistants: Schulz, S.
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